From: Ben Goertzel (firstname.lastname@example.org)
Date: Mon Mar 29 2004 - 07:25:50 MST
> One appealing answer to this question of the prior is to
> define the prior probability of a possible universe being
> base reality as the inverse of the complexity of its laws of
> physics. This could be formalized as P(X) =
> n^-K(X) where X is a possible universe, n is the size of the
> alphabet of the language of a formal set theory, and K(X) is
> length of the shortest definition in this language of a set
> isomorphic to X. (Those of you familiar with algorithmic
> complexity theory might notice that K(X) is just a
> generalization of algorithmic complexity, to sets, and to
> non-constructive descriptions. The reason for this
> generalization is to
> avoid assuming that base reality must be discrete and computable.)
But of course, using this method, for each formal set theory, you can
only distinguish countably many different possible universes -- even
though some of these may be "uncomputable" according to the
computational model adopted.
> The lack of a objective criteria for choosing a formal set
> theory for this purpose leads me to wonder if perhaps the
> choice of a prior is a subjective one, similar to the
> "choice" of a supergoal in the presumed absence of objective
> morality. In case it is, shouldn't we try to answer this
> question before building an SI?
Clearly, the notion of "base reality" as an objective entity is
Rather, all we have is "apparently base reality, based on the
perceptions and cognitions of mind M, or of minds in class M."
A mind M-1 with greater capability may be able to detect that M's "base
reality" isn't really a "base reality" at all.
One could surely prove that, for any mind, there are some possible
simulations it could be living in, where it could never detect it was in
a simulation -- yet an abler mind could. This would be yet another
Godel theorem varient.
I agree that there is no way to "objectively" choose a prior over the
space of possible universes. This is essentially the problem at the
heart of the Bayesian approach to induction (in the general, Hume-ean
sense). You need a prior distribution on hypothesis space (in this
case, hypotheses about which universe exists).
One approach that's been discussed on this list a lot is algorithmic
information, the Solomonoff-Levin measure, etc. However, this depends
on the base computational model.
One approach here, following Hume, is to take "human nature" as a base
computational model -- so that prior probability becomes "simplicity to
the human mind." Or, taking a page from Eliezer's notion of
humane-ness, perhaps "simplicity to some sort of idealized collective
human mind." But I don't find this very satisfactory.
I'm happier applying the human intuition for simplicity to the *choice
of computational model*. Hence, I prefer a base computational model
involving very simple computational operations, such as the S and K
combinator.... See e.g.
for an apparently very-close-to-minimal formulation of universal
As it happens, this ties in with Novamente AI, since our system uses
combinatory logic as part of its knowledge representation.
-- Ben G
-- Ben G
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